H-ARQ is a transmission scheme that is widely used in many wireless communication systems to ensure successful data transmission. In H-ARQ, a receiver sends feedback to a transmitter, indicating successful or unsuccessful receipt of a data packet, so that the transmitter retransmits a failed data packet.
MIMO is a technique used to increase data rate and system throughput. In a MIMO system, a transmitter and a receiver use multiple antennas for transmission and reception so that multiple data streams are transmitted simultaneously via multiple antennas.
Different H-ARQ transmission schemes have been proposed for MIMO systems. In a conventional simple repetitive H-ARQ scheme for a MIMO system, symbols are simply repeated in a subsequent transmission if the initial transmission fails. Table 1 shows signal transmissions in accordance with the conventional simple repetitive H-ARQ for a 2×2 MIMO system.
TABLE 1Antenna 1Antenna 2first transmissionx1x2second transmissionx1x2
A space time block code (STBC)-based H-ARQ scheme for a MIMO system has been proposed for evolved universal terrestrial radio access (EUTRA). Table 2 shows signal transmissions in accordance with the STBC-based H-ARQ for a 2×2 MIMO system.
TABLE 2Antenna 1Antenna 2first transmissionx1x2second transmissionx2*−x1*
In a 2×2 MIMO system, as an exemplary MIMO system, a received signal may be expressed as follows:
                                          (                                                                                                      y                      1                                        ⁡                                          (                      t                      )                                                                                                                                                              y                      2                                        ⁡                                          (                      t                      )                                                                                            )                    =                                                    (                                                                                                                              h                          11                                                ⁡                                                  (                          t                          )                                                                                                                                                              h                          12                                                ⁡                                                  (                          t                          )                                                                                                                                                                                                  h                          21                                                ⁡                                                  (                          t                          )                                                                                                                                                              h                          22                                                ⁡                                                  (                          t                          )                                                                                                                    )                            ⁢                              (                                                                                                    x                        1                                                                                                                                                x                        2                                                                                            )                                      +                          (                                                                                                                  n                        1                                            ⁡                                              (                        t                        )                                                                                                                                                                                n                        2                                            ⁡                                              (                        t                        )                                                                                                        )                                      ;                            Equation        ⁢                                  ⁢                  (          1          )                    where t is an index in time, yi, i=1, 2, is received signals at receive antenna i, hij, i,j=1, 2, is channel coefficients between receive antenna i and transmit antenna j, xj, j=1, 2, is transmitted signals at transmit antenna j, and ni, i=1, 2, is a noise at receive antenna i. It is assumed that the channel is quasi-static so that the channel coefficients are same during retransmission of the failed packet and the time index on the channel coefficients will be dropped hereinafter.
At a high signal-to-noise ratio (SNR), the SNR for the two data streams after linear minimum mean square error (LMMSE) detection is written as follows:
                                                        SNR              ⁡                              (                                  x                  1                                )                                      =                                          (                                                      d                    1                                    -                                                                                                            c                                                                    2                                                              d                      2                                                                      )                            ⁢                                                E                  s                                                  N                  0                                                              ;                ⁢                                  ⁢        and                            Equation        ⁢                                  ⁢                  (          2          )                                                              SNR            ⁡                          (                              x                2                            )                                =                                    (                                                d                  2                                -                                                                                                  c                                                              2                                                        d                    1                                                              )                        ⁢                                          E                s                                            N                0                                                    ;                            Equation        ⁢                                  ⁢                  (          3          )                    where Es is symbol energy, N0 is noise power spectrum density, andd1=|h11|2+|h21|2;  Equation (4)d2=|h12|2+|h22|2;  and Equation (5)c=h11*h12+h22h21*.  Equation (6)
An SNR ratio between two data streams is:
                                          SNR            ⁡                          (                              x                1                            )                                            SNR            ⁡                          (                              x                2                            )                                      =                                            d              1                                      d              2                                .                                    Equation        ⁢                                  ⁢                  (          7          )                    The SNR ratio in Equation (7) or its variation is used as criteria in assigning a modulation and coding scheme (MCS) for each of the data streams.
For the conventional simple repetitive H-ARQ transmission, the received signal in the retransmission is written as follows:
                              (                                                                                          y                    1                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                                                                            y                    2                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                )                =                                            (                                                                                          h                      11                                                                                                  h                      12                                                                                                                                  h                      21                                                                                                  h                      22                                                                                  )                        ⁢                          (                                                                                          x                      1                                                                                                                                  x                      2                                                                                  )                                +                                    (                                                                                                                  n                        1                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                                                                                                n                        2                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                        )                        .                                              Equation        ⁢                                  ⁢                  (          8          )                    
Combining Equation (1) and Equation (8) results in:
                              (                                                                                          y                    1                                    ⁡                                      (                    t                    )                                                                                                                                            y                    2                                    ⁡                                      (                    t                    )                                                                                                                                            y                    1                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                                                                            y                    2                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                )                =                                            (                                                                                          h                      11                                                                                                  h                      12                                                                                                                                  h                      21                                                                                                  h                      22                                                                                                                                  h                      11                                                                                                  h                      12                                                                                                                                  h                      21                                                                                                  h                      22                                                                                  )                        ⁢                          (                                                                                          x                      1                                                                                                                                  x                      2                                                                                  )                                +                                    (                                                                                                                  n                        1                                            ⁡                                              (                        t                        )                                                                                                                                                                                n                        2                                            ⁡                                              (                        t                        )                                                                                                                                                                                n                        1                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                                                                                                n                        2                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                        )                        .                                              Equation        ⁢                                  ⁢                  (          9          )                    
At a high SNR, the SNRs for the two data streams, after LMMSE detection, are as follows:
                                                        SNR              ⁡                              (                                  x                  1                                )                                      =                          2              ⁢                              (                                                      d                    1                                    -                                                                                                            c                                                                    2                                                              d                      2                                                                      )                            ⁢                                                E                  s                                                  N                  0                                                              ;                ⁢                                  ⁢        and                            Equation        ⁢                                  ⁢                  (          10          )                                                  SNR          ⁡                      (                          x              2                        )                          =                  2          ⁢                      (                                          d                2                            -                                                                                        c                                                        2                                                  d                  1                                                      )                    ⁢                                                    E                s                                            N                0                                      .                                              Equation        ⁢                                  ⁢                  (          11          )                    The SNRs are 3 dB higher than initial transmission. The SNR ratio between the two data streams is the same as the initial transmission.
For the STBC-based H-ARQ, the signal received for the retransmission is written as follows:
                              (                                                                                          y                    1                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                                                                            y                    2                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                )                =                                            (                                                                                          h                      11                                                                                                  h                      12                                                                                                                                  h                      21                                                                                                  h                      22                                                                                  )                        ⁢                          (                                                                                          x                      2                      *                                                                                                                                  -                                              x                        1                        *                                                                                                        )                                +                                    (                                                                                                                  n                        1                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                                                                                                n                        2                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                        )                        .                                              Equation        ⁢                                  ⁢                  (          12          )                    
Combining Equation (12) and Equation (1) results in:
                              (                                                                                          y                    1                                    ⁡                                      (                    t                    )                                                                                                                                            y                    2                                    ⁡                                      (                    t                    )                                                                                                                                            y                    1                    *                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                                                                            y                    2                    *                                    ⁡                                      (                                          t                      +                      1                                        )                                                                                )                =                                            (                                                                                          h                      11                                                                                                  h                      12                                                                                                                                  h                      21                                                                                                  h                      22                                                                                                                                  -                                              h                        12                        *                                                                                                                        h                      11                      *                                                                                                                                  -                                              h                        22                        *                                                                                                                        h                      21                      *                                                                                  )                        ⁢                          (                                                                                          x                      1                                                                                                                                  x                      2                                                                                  )                                +                                    (                                                                                                                  n                        1                                            ⁡                                              (                        t                        )                                                                                                                                                                                n                        2                                            ⁡                                              (                        t                        )                                                                                                                                                                                n                        1                        *                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                                                                                                n                        2                        *                                            ⁡                                              (                                                  t                          +                          1                                                )                                                                                                        )                        .                                              Equation        ⁢                                  ⁢                  (          13          )                    
At high SNR, the SNRs after LMMSE detector for the two data streams are as follows:
                              SNR          ⁡                      (                          x              1                        )                          =                              SNR            ⁡                          (                              x                2                            )                                ≈                                    (                                                d                  1                                +                                  d                  2                                            )                        ⁢                                                            E                  s                                                  N                  0                                            .                                                          Equation        ⁢                                  ⁢                  (          14          )                    Comparing Equations (10), (11) and (14), it can be seen that STBC-based H-ARQ increases the total SNR across the two data streams compared to the simple repetitive H-ARQ when the cross term |c|≠0, which is generally true for a random MIMO channel.
However, in many practical systems, to achieve the maximum capacity offered by the MIMO channel, a data rate assigned to each spatial data stream is controlled separately according to its own SNR. This scheme is often referred to as per-antenna rate control (PARC). At the initial transmission, the transmitter, (e.g., a Node-B), would allocate a higher modulation and coding scheme (MCS) to the antenna with a higher SNR and allocate a lower MCS to the antenna with a lower SNR. Since the MCS is often kept the same for each antenna when retransmission occurs, it is desirable to keep the same SNR ratio between the antennas after retransmissions. However, the STBC-based H-ARQ scheme equalizes the SNR across all data streams after packet combining as shown in Equation (14). Therefore, the STBC-based H-ARQ scheme is not suitable for systems that adaptively change data rate per spatial stream, (e.g., PARC).